lower bound: | 71 |
upper bound: | 74 |
Construction of a linear code [117,8,71] over GF(3): [1]: [118, 8, 72] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 2, 1, 2, 2, 2, 2, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 2, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 2, 2, 1, 2, 1, 2, 2, 0, 0, 1, 2, 2, 2, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 0, 1, 0, 2, 0 ] [ 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 0, 2, 2, 0, 0, 0, 2, 1, 1, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 0, 2, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 2, 0, 0, 1, 0, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 1, 0, 2, 1, 0, 1, 0, 1, 2, 0, 2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 1, 1, 2, 2, 1, 0, 2, 1, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2, 1, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0, 0, 2, 1, 1, 2, 1, 2, 2, 2, 0, 0, 2, 1, 1, 1, 1, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 2, 0, 1, 2, 2, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 0, 2, 1, 2, 1, 1, 0, 2, 1, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 2, 1, 1, 0, 0, 1, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 0, 1, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1 ] [2]: [117, 8, 71] Linear Code over GF(3) Puncturing of [1] at { 118 } last modified: 2008-11-06
Lb(117,8) = 70 is found by shortening of: Lb(119,10) = 70 is found by truncation of: Lb(121,10) = 72 dB Ub(117,8) = 74 follows by a one-step Griesmer bound from: Ub(42,7) = 24 follows by a one-step Griesmer bound from: Ub(17,6) = 8 is found by considering truncation to: Ub(16,6) = 7 vE2
vE2: M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory 41 (1995) 800-805.
Notes
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